an:00916201
Zbl 0860.11070
Dragovi??, B. G.
Rational summation of \(p\)-adic series
EN
Theor. Math. Phys. 100, No. 3, 1055-1064 (1994) and Teor. Mat. Fiz. 100, No. 3, 342-353 (1994).
00030147
1994
j
11S80 30B10 81T30
\(p\)-adic power series; \(p\)-adic quantum field theory; convergence; rational value
Certain \(p\)-adic power series, their domain of convergence, and the problem as to whether the sum is rational for some rational value of the variable, are discussed. Examples of such series are given. In the introduction the connection with \(p\)-adic quantum field theory is explained.
Note of the reviewer: In section 5 of the paper it is stated that \(\sum n!\) cannot be rational in every \(\mathbb{Q}_p\) \((p\) prime). However, according to the quoted reference, it is only known that the sum cannot be rational in every \(\mathbb{Q}_n\) \((n \in \mathbb{N},\;n \geq 2)\).
W.Schikhof (Nijmegen)